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Are there any special methods and rules for selecting bases in the basic theorem of plane vectors in senior high school mathematics?
Of course, the standard basis needs two mutually perpendicular unit vectors.

If it is non-standard, it depends on which expression is good. Generally speaking, it will be based on the two basic expression vectors given in the title. If all other vectors in a topic are required to be represented by two vectors, A and B, of course, A and B are bases. Non-standard is actually not coordinate point multiplication, so it is more flexible and simple in setting cardinal number.